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John Derbyshire

Prime obsession : Bernhard Riemann and the greatest unsolved problem in mathematics

The Riemann hypothesis is a conjecture which has resisted attempts to prove it for a century and a half, and so is of great interest to the mathematical community. In 'Prime Obsession' John Derbyshire takes a dual approach to this topic, alternating mathematical chapters with chapters on the Riemann's life and the history of the hypothesis. I think that this works extremely well - if you are finding the maths hard going, then you have a break with a historical chapter (and vice-versa of course). I feel that it is a structure which other authors would do well to consider applying to their subject.

The structure of the book also means that the maths can proceed independently of the history. Other books have a tendency to give a superficial coverage of the nature of the hypothesis early on. In this book the subject is dealt with more gradually, to give a fuller appreciation of link between prime numbers and the zeroes of the complex valued zeta function. The book is aimed at the non-technical reader, but I feel that to reach the end of the book you will really need to be reasonably comfortable with mathematics, at least up to the later parts of school mathematics.

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Hardcover 448 pages
ISBN: 0309085497
Salesrank: 309860
Weight:1.25 lbs

Published: 2003 Joseph Henry Press

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Amazon.co.uk info

Hardcover 448 pages
ISBN: 0309085497
Salesrank: 300742
Weight:1.25 lbs

Published: 2003 Henry (Joseph) Press

Amazon price £14.99

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Hardcover 448 pages
ISBN: 0309085497
Salesrank: 253511
Weight:1.25 lbs

Published: 2003 National Academy Press

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Product Description
In August 1859 Bernhard Riemann, a little-known 32-year old mathematician, presented a paper to the Berlin Academy titled: "On the Number of Prime Numbers Less Than a Given Quantity." In the middle of that paper, Riemann made an incidental remark -- a guess, a hypothesis. What he tossed out to the assembled mathematicians that day has proven to be almost cruelly compelling to countless scholars in the ensuing years. Today, after 150 years of careful research and exhaustive study, the question remains. Is the hypothesis true or false? Riemann’s basic inquiry, the primary topic of his paper, concerned a straightforward but nevertheless important matter of arithmetic--defining a precise formula to track and identify the occurrence of prime numbers. But it is that incidental remark -- the Riemann Hypothesis -- that is the truly astonishing legacy of his 1859 paper. Because Riemann was able to see beyond the pattern of the primes to discern traces of something mysterious and mathematically elegant shrouded in the shadows--subtle variations in the distribution of those prime numbers. Brilliant for its clarity, astounding for its potential consequences, the Hypothesis took on enormous importance in mathematics. Indeed, the successful solution to this puzzle would herald a revolution in prime number theory. Proving or disproving it became the greatest challenge of the age. It has become clear that the Riemann Hypothesis, whose resolution seems to hang tantalizingly just beyond our grasp, holds the key to a variety of scientific and mathematical investigations. The making and breaking of modern codes, which depend on the properties of the prime numbers, have roots in the Hypothesis. In a series of extraordinary developments during the 1970s, it emerged that even the physics of the atomic nucleus is connected in ways not yet fully understood to this strange conundrum. Hunting down the solution to the Riemann Hypothesis has become an obsession for many -- the veritable "great white whale" of mathematical research. Yet despite determined efforts by generations of mathematicians, the Riemann Hypothesis defies resolution. Alternating passages of extraordinarily lucid mathematical exposition with chapters of elegantly composed biography and history, Prime Obsession is a fascinating and fluent account of an epic mathematical mystery that continues to challenge and excite the world. Posited a century and a half ago, Riemann’s hypothesis is an intellectual feast for the cognoscenti and the curious alike. Not just a story of numbers and calculations, Prime Obsession is the engrossing tale of a relentless hunt for an elusive proof -- and those who have been consumed by it.

Product Description

In August 1859 Bernhard Riemann, a little-known 32-year old mathematician, presented a paper to the Berlin Academy titled: "On the Number of Prime Numbers Less Than a Given Quantity." In the middle of that paper, Riemann made an incidental remark -- a guess, a hypothesis. What he tossed out to the assembled mathematicians that day has proven to be almost cruelly compelling to countless scholars in the ensuing years. Today, after 150 years of careful research and exhaustive study, the question remains. Is the hypothesis true or false?

Riemann’s basic inquiry, the primary topic of his paper, concerned a straightforward but nevertheless important matter of arithmetic--defining a precise formula to track and identify the occurrence of prime numbers. But it is that incidental remark -- the Riemann Hypothesis -- that is the truly astonishing legacy of his 1859 paper. Because Riemann was able to see beyond the pattern of the primes to discern traces of something mysterious and mathematically elegant shrouded in the shadows--subtle variations in the distribution of those prime numbers. Brilliant for its clarity, astounding for its potential consequences, the Hypothesis took on enormous importance in mathematics. Indeed, the successful solution to this puzzle would herald a revolution in prime number theory. Proving or disproving it became the greatest challenge of the age.

It has become clear that the Riemann Hypothesis, whose resolution seems to hang tantalizingly just beyond our grasp, holds the key to a variety of scientific and mathematical investigations. The making and breaking of modern codes, which depend on the properties of the prime numbers, have roots in the Hypothesis. In a series of extraordinary developments during the 1970s, it emerged that even the physics of the atomic nucleus is connected in ways not yet fully understood to this strange conundrum. Hunting down the solution to the Riemann Hypothesis has become an obsession for many -- the veritable "great white whale" of mathematical research. Yet despite determined efforts by generations of mathematicians, the Riemann Hypothesis defies resolution.

Alternating passages of extraordinarily lucid mathematical exposition with chapters of elegantly composed biography and history, Prime Obsession is a fascinating and fluent account of an epic mathematical mystery that continues to challenge and excite the world. Posited a century and a half ago, Riemann’s hypothesis is an intellectual feast for the cognoscenti and the curious alike. Not just a story of numbers and calculations, Prime Obsession is the engrossing tale of a relentless hunt for an elusive proof -- and those who have been consumed by it.

Prime numbers and Riemann *****
Very good book, easy to read, no previous knowledge on math is needed but just secondary.

Prime numbers and Riemann *****

Very good book, easy to read, no previous knowledge on math is needed but just secondary.

A masterpiece of its genre *****
There are a number of authors who have tried to esplain difficult scientific or mathematical problems to non-expert readers. I have read and enjoyed many such books. Thus far, Derbyshire is the master.

A masterpiece of its genre *****

There are a number of authors who have tried to esplain difficult scientific or mathematical problems to non-expert readers. I have read and enjoyed many such books. Thus far, Derbyshire is the master.

A great book, which I'll explain later in the review. ****
This is a fine book that lays out clearly Riemann's life and times and the mathematical work he did, but I'll explain more about that later in the review. The author certainly knows his subject matter and it thoroughly researched, which I'll touch on a little later. The only thing that drove me to distraction was that at least 2 times in every chapter he would make a point, then say something like "I'll explain more about this in just a bit" or "More about this later" or "In chapter 12 I'll touch on this again". I'm not kidding, it happened EVERY chapter and after a while it got annoying....but I'll show you more about that in my other review. Still, a great read and required reading for anyone into mathematics and number theory.

A great book, which I'll explain later in the review. ****

This is a fine book that lays out clearly Riemann's life and times and the mathematical work he did, but I'll explain more about that later in the review.

The author certainly knows his subject matter and it thoroughly researched, which I'll touch on a little later. The only thing that drove me to distraction was that at least 2 times in every chapter he would make a point, then say something like "I'll explain more about this in just a bit" or "More about this later" or "In chapter 12 I'll touch on this again". I'm not kidding, it happened EVERY chapter and after a while it got annoying....but I'll show you more about that in my other review.

Still, a great read and required reading for anyone into mathematics and number theory.

A rambling, long winded book that never makes a point succinctly. 2.5 stars. **
The Prime Number Theorem and its related consequences is a fascinating subject. This book however is a long winded, very poorly written attempt. The author never seems to be able to make a point clearly and succinctly. Instead we are treated to a ramble that confuses more than elaborates. For example the presentation on functions is very poorly done. I have seen basic algebra texts explain the idea of functions far better than in this book. To make matters worse the author takes about ten pages to explain the beautiful idea of a function thus killing a sublime truth. Sorry to say but far better general math books abound. Take a look at Journey Through Genius.

A rambling, long winded book that never makes a point succinctly. 2.5 stars. **

The Prime Number Theorem and its related consequences is a fascinating subject. This book however is a long winded, very poorly written attempt. The author never seems to be able to make a point clearly and succinctly. Instead we are treated to a ramble that confuses more than elaborates. For example the presentation on functions is very poorly done. I have seen basic algebra texts explain the idea of functions far better than in this book. To make matters worse the author takes about ten pages to explain the beautiful idea of a function thus killing a sublime truth.

Sorry to say but far better general math books abound. Take a look at Journey Through Genius.

Simply breathtaking *****
Wauw, never thought the prime principles and theories behind it could be explained so well and most of all so easy to understand. With this book, the writer makes one of the most mysterious and complex theories in mathematics easy to understand for the common man. Simply great!

Simply breathtaking *****

Wauw, never thought the prime principles and theories behind it could be explained so well and most of all so easy to understand.
With this book, the writer makes one of the most mysterious and complex theories in mathematics easy to understand for the common man.
Simply great!

Challenging, but worth it *****
The great German mathematician, David Hilbert was once asked what question would he ask if could come back in 500 years' time. His response was immidiate: "Has anyone proved the Riemann Hypothesis?" Reading this book, you'll understand why Hilbert didn't hesitate. This is by far the most 'mathematical' of the popular books on the RH, and if you are a mathematical numpty like me, you might be discouraged at first glance. Don't be!!! Derbyshire actually does a really good job of walking you through it. It's an extremely rewarding read. I particularly like the way he also wove in the politcal and social upheavals that were taking place in Germany and Europe in general at the time that Riemann was formulating his hypothesis.

Challenging, but worth it *****

The great German mathematician, David Hilbert was once asked what question would he ask if could come back in 500 years' time. His response was immidiate:

"Has anyone proved the Riemann Hypothesis?"

Reading this book, you'll understand why Hilbert didn't hesitate. This is by far the most 'mathematical' of the popular books on the RH, and if you are a mathematical numpty like me, you might be discouraged at first glance. Don't be!!! Derbyshire actually does a really good job of walking you through it. It's an extremely rewarding read. I particularly like the way he also wove in the politcal and social upheavals that were taking place in Germany and Europe in general at the time that Riemann was formulating his hypothesis.

Interesting ***
I enjoyed the first half of the book - which provides a good background of the subject matter. Towards the latter half I grew weary of the author's style of writing and also found all the non-mathematical anecdotes annoying. I think the author's effort to dumb everything down ultimately destroys the point of the book. But this is a good starting point for a layperson who is interested in the Riemann hypothesis. I yearn for a more mathematical book, though.

Interesting ***

I enjoyed the first half of the book - which provides a good background of the subject matter. Towards the latter half I grew weary of the author's style of writing and also found all the non-mathematical anecdotes annoying. I think the author's effort to dumb everything down ultimately destroys the point of the book. But this is a good starting point for a layperson who is interested in the Riemann hypothesis. I yearn for a more mathematical book, though.

A popularisation the focuses on the actual mathematics *****
Most books of this kind don't bother to try to talk about the actual maths, so they waffle on about the mathematicians, which is something like watching interviews of rock stars when you want to be seeing them performing. This book is an exception - it does its mightiest to actually explain the innards of the conjecture and goes some way towards achieving its aim. No quibble - this is the best book on its subject that's available at the moment, unless you're going for something more technical.

A popularisation the focuses on the actual mathematics *****

Most books of this kind don't bother to try to talk about the actual maths, so they waffle on about the mathematicians, which is something like watching interviews of rock stars when you want to be seeing them performing.

This book is an exception - it does its mightiest to actually explain the innards of the conjecture and goes some way towards achieving its aim.

No quibble - this is the best book on its subject that's available at the moment, unless you're going for something more technical.

Do not buy any others *****
I have read this book and one of the other two popularisations about the Riemann hypothesis. Instead of interviewing mathematicians who may be near to solving it or writing around the subject, this book actually works through the mathematics of Riemann's 1859 paper. It emphasises the centrality of Riemann's other parts of the paper apart from the famous Hypothesis and so helps to explain why some 30 years later that mathematicians were able to prove the Prime Number Theorem, independently of the truth or otherwise of the famous hypothesis: roughly that as numbers get larger the number of primes less than that number tends to about the number divided by its logarithm (base e). The reason is because of the techniques that Riemann invented in his paper. Riemann's starting point was to generalise Euler's formula which relates the sum of a reciprocals of natural numbers: 1+1/2+1/3+1/4+... to the product of the inverses of the prime numbers. Derbyshire's explanation is far clearer than others and even I was able to understand it. This book is precise and clear: one really feels that one has some insight into an astonishing piece of creative mathematical work by the time one has read the book. That alone in my opinion should qualify it as one of the greatest pieces of popular science writing of this or any other decade. This book needs to be more actively marketed: whatever its faults, the author has made a genuine attempt to really explain a great piece of science technically to a non -technical audience, rather than just waffling around the subject and making us all feel these things are so far above our heads we will never understand them in any way. This courage on the author's part needs to be more widely feted. I cannot do more than endorse the other reviewers' praise for this classic-to-be.

Do not buy any others *****

I have read this book and one of the other two popularisations about the Riemann hypothesis. Instead of interviewing mathematicians who may be near to solving it or writing around the subject, this book actually works through the mathematics of Riemann's 1859 paper.
It emphasises the centrality of Riemann's other parts of the paper apart from the famous Hypothesis and so helps to explain why some 30 years later that mathematicians were able to prove the Prime Number Theorem, independently of the truth or otherwise of the famous hypothesis: roughly that as numbers get larger the number of primes less than that number tends to about the number divided by its logarithm (base e). The reason is because of the techniques that Riemann invented in his paper.

Riemann's starting point was to generalise Euler's formula which relates the sum of a reciprocals of natural numbers: 1+1/2+1/3+1/4+... to the product of the inverses of the prime numbers. Derbyshire's explanation is far clearer than others and even I was able to understand it.

This book is precise and clear: one really feels that one has some insight into an astonishing piece of creative mathematical work by the time one has read the book. That alone in my opinion should qualify it as one of the greatest pieces of popular science writing of this or any other decade.

This book needs to be more actively marketed: whatever its faults, the author has made a genuine attempt to really explain a great piece of science technically to a non -technical audience, rather than just waffling around the subject and making us all feel these things are so far above our heads we will never understand them in any way. This courage on the author's part needs to be more widely feted.

I cannot do more than endorse the other reviewers' praise for this classic-to-be.

A fabulous read *****
Having read Marcus de Sautoy's book on prime numbers my appetite was sufficiently wetted to go out and by Edwards book on the Zeta function. Unfirtunately one look at this told me I wasn't going to be able to get through it. I picked this book up by accident and it was fascinating in that the author goes through the whole of Riemanns 1859 paper and explains the whole theorem, which is quite breathtaking in its brilliance. He loses it a bit at the end, but he can be forgiven for that as it does become very complicated. That combined with the way he weaves the history of prime numbers in alternative chapters makes this a thoroughly enjoyable book. If you like maths go and buy it!

A fabulous read *****

Having read Marcus de Sautoy's book on prime numbers my appetite was sufficiently wetted to go out and by Edwards book on the Zeta function. Unfirtunately one look at this told me I wasn't going to be able to get through it. I picked this book up by accident and it was fascinating in that the author goes through the whole of Riemanns 1859 paper and explains the whole theorem, which is quite breathtaking in its brilliance. He loses it a bit at the end, but he can be forgiven for that as it does become very complicated. That combined with the way he weaves the history of prime numbers in alternative chapters makes this a thoroughly enjoyable book. If you like maths go and buy it!

Complex Math Made Very Understandable and Interesting *****
Although this book deals with a subject that no-one would sensibly place in a category below "Very Advanced," John Derbyshire treats his subject as well as any math author I've ever read, and I've read a lot of math books over the past 40-some years. My formal math education ended after a standard introductory calculus course as an undergrad. However, I have always been, and remain, extremely interested in math -- a math aficianado if you will. As such, I've self-taught myself a lot of math -- including a lot of very advanced math -- over the past 40 years; ergo, my reading of a great many math books. And without doubt, Derbyshire's book is the finest math book I've yet to read. I suspect Derbyshire started with the hypothesis that his readers are not familiar (or only familiar in a passing sense) with high-level, advanced math, and perhaps might even suffer from math anxiety. Any such readers, however, should have absolutely no fears. Derbyshire's exposition is superb. He clearly defines everything the reader needs to know to grasp AND understand fully the more advanced parts of the book. The book is clearly well designed to convey the information he wants or needs of convey and masterfully explains what would otherwise be quite difficult to understand. Without any doubt this is by far the best book on any advanced and complicated subject -- the best book on ANY math subject (including a book on something as simple as how to add one and one) -- I have ever read. Without sacrificing the complexity of the subject, Derbyshire has written his book in a very readable and interesting manner. And he does all this while making the subject so interesting you can hardly wait for someone to finally prove Riemann's Hypothesis and Riemann's zeta function so we can read Derbyshire's account of that landmark event in the history of mathematics.

Complex Math Made Very Understandable and Interesting *****

Although this book deals with a subject that no-one would sensibly place in a category below "Very Advanced," John Derbyshire treats his subject as well as any math author I've ever read, and I've read a lot of math books over the past 40-some years.

My formal math education ended after a standard introductory calculus course as an undergrad. However, I have always been, and remain, extremely interested in math -- a math aficianado if you will. As such, I've self-taught myself a lot of math -- including a lot of very advanced math -- over the past 40 years; ergo, my reading of a great many math books. And without doubt, Derbyshire's book is the finest math book I've yet to read.

I suspect Derbyshire started with the hypothesis that his readers are not familiar (or only familiar in a passing sense) with high-level, advanced math, and perhaps might even suffer from math anxiety. Any such readers, however, should have absolutely no fears. Derbyshire's exposition is superb. He clearly defines everything the reader needs to know to grasp AND understand fully the more advanced parts of the book. The book is clearly well designed to convey the information he wants or needs of convey and masterfully explains what would otherwise be quite difficult to understand.

Without any doubt this is by far the best book on any advanced and complicated subject -- the best book on ANY math subject (including a book on something as simple as how to add one and one) -- I have ever read.

Without sacrificing the complexity of the subject, Derbyshire has written his book in a very readable and interesting manner. And he does all this while making the subject so interesting you can hardly wait for someone to finally prove Riemann's Hypothesis and Riemann's zeta function so we can read Derbyshire's account of that landmark event in the history of mathematics.

splendid (though heavy math) *****
This book should be the first one to appear in Amazon's listings for the Riemann Hypothesis, yet doesn't even appear in the top ten. It gives fascinating historical background to a very real Riemann and his friends, traces developments to the present day in a conversational tone, and somehow manages to take the reader through the details of what the RH says so that you actually understand it. Recommended with one reservation; to understand the chapters (every other one) which bring one to understand the RH, you will need to make a considerable investment in reading and rereading to make it. That is not for the faint of heart. However, the other half of the book can be enjoyed by anyone who likes general science history books.

splendid (though heavy math) *****

This book should be the first one to appear in Amazon's listings for the Riemann Hypothesis, yet doesn't even appear in the top ten. It gives fascinating historical background to a very real Riemann and his friends, traces developments to the present day in a conversational tone, and somehow manages to take the reader through the details of what the RH says so that you actually understand it. Recommended with one reservation; to understand the chapters (every other one) which bring one to understand the RH, you will need to make a considerable investment in reading and rereading to make it. That is not for the faint of heart. However, the other half of the book can be enjoyed by anyone who likes general science history books.

What a piece of work a man is! *****
"Prime Obsession" is a fascinating book for several reasons: the author explains a difficult topic with such clarity that it's simply amazing. For those who are more skilled in math, this book would also be very enjoyable to read, except that they might find some of his explanations redundant because he really assumes that the we don't know anything (and I mean anything!). Mr. Derbyshire obviously understands the topic quite well himself. He has written an amazing book for everyone to enjoy. 200 years since Riemann first presented the problem, we are still desperately trying to solve it, and one day, you never know... what a piece of work a man is!

What a piece of work a man is! *****

"Prime Obsession" is a fascinating book for several reasons: the author explains a difficult topic with such clarity that it's simply amazing. For those who are more skilled in math, this book would also be very enjoyable to read, except that they might find some of his explanations redundant because he really assumes that the we don't know anything (and I mean anything!).
Mr. Derbyshire obviously understands the topic quite well himself. He has written an amazing book for everyone to enjoy.
200 years since Riemann first presented the problem, we are still desperately trying to solve it, and one day, you never know... what a piece of work a man is!

An Excellent Read, Highly Recommended *****
Prime Obsession is an excellent popularization of the Riemann Hypothesis. I found John Derbyshire's presentation of the math to be very approachable by non-mathematicians like myself. It's taken slow, one basic step at a time, and spread across a well written and fascinating history of Bernhard Riemann and other key players. Simply put, you do not need an advance degree in mathematics to enjoy this book. My math bakground is limited to 2 semesters of calculus 20 years ago and I haven't used it since. For me, John Derbyshire's approach was both refreshing and entertaining. If you've got even the faintest interest in math, you will find this book rewarding.

An Excellent Read, Highly Recommended *****

Prime Obsession is an excellent popularization of the Riemann Hypothesis. I found John Derbyshire's presentation of the math to be very approachable by non-mathematicians like myself. It's taken slow, one basic step at a time, and spread across a well written and fascinating history of Bernhard Riemann and other key players. Simply put, you do not need an advance degree in mathematics to enjoy this book.

My math bakground is limited to 2 semesters of calculus 20 years ago and I haven't used it since. For me, John Derbyshire's approach was both refreshing and entertaining. If you've got even the faintest interest in math, you will find this book rewarding.

Good overview *****
This book accomplishes two things very well. It explains the history behind the Riemann Hypothesis and also the relevant mathematics. I like how the author structured the book and also how he simplified the math somewhat. However, the math contained in this book can be challenging if you don't have any background. I would recommend a basic understanding of calculus if you want to understand the math. However, the math is kept separate from the history, so if you just want a historical overview, then this book will also work well. I recommend this book to anyone interested in math and math history.

Good overview *****

This book accomplishes two things very well. It explains the history behind the Riemann Hypothesis and also the relevant mathematics. I like how the author structured the book and also how he simplified the math somewhat. However, the math contained in this book can be challenging if you don't have any background. I would recommend a basic understanding of calculus if you want to understand the math. However, the math is kept separate from the history, so if you just want a historical overview, then this book will also work well. I recommend this book to anyone interested in math and math history.